Question

in triangle def altitude ds bisects the side ef, prove that def is an isosceles triangle

Answer 1

Answer:

consider the triangles DES and DFS

ES=FS ( bisector )

angle(DSE)=angle(DSF)=90° (altitude)

DS=DS( common side )

therefore by SAS rule triangle DES and DFS are congruent

we can therefore say sides DE=DF implies DEF is an isoceles triangle